$K$-means clustering is a widely used machine learning method for identifying patterns in large datasets. Recently, semidefinite programming (SDP) relaxations have been proposed for solving the $K$-means optimization problem, which enjoy strong statistical optimality guarantees. However, the prohibitive cost of implementing an SDP solver renders these guarantees inaccessible to practical datasets. In contrast, nonnegative matrix factorization (NMF) is a simple clustering algorithm widely used by machine learning practitioners, but it lacks a solid statistical underpinning and theoretical guarantees. In this paper, we consider an NMF-like algorithm that solves a nonnegative low-rank restriction of the SDP-relaxed $K$-means formulation using a nonconvex Burer--Monteiro factorization approach. The resulting algorithm is as simple and scalable as state-of-the-art NMF algorithms while also enjoying the same strong statistical optimality guarantees as the SDP. In our experiments, we observe that our algorithm achieves significantly smaller mis-clustering errors compared to the existing state-of-the-art while maintaining scalability.
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Graph Neural Networks (GNNs) have emerged as the leading deep learning models for graph-based representation learning. However, the training and inference of GNNs on large graphs remain resource-intensive, impeding their utility in real-world scenarios and curtailing their applicability in deeper and more sophisticated GNN architectures. To address this issue, the Graph Lottery Ticket (GLT) hypothesis assumes that GNN with random initialization harbors a pair of core subgraph and sparse subnetwork, which can yield comparable performance and higher efficiency to that of the original dense network and complete graph. Despite that GLT offers a new paradigm for GNN training and inference, existing GLT algorithms heavily rely on trial-and-error pruning rate tuning and scheduling, and adhere to an irreversible pruning paradigm that lacks elasticity. Worse still, current methods suffer scalability issues when applied to deep GNNs, as they maintain the same topology structure across all layers. These challenges hinder the integration of GLT into deeper and larger-scale GNN contexts. To bridge this critical gap, this paper introduces an $\textbf{A}$daptive, $\textbf{D}$ynamic, and $\textbf{A}$utomated framework for identifying $\textbf{G}$raph $\textbf{L}$ottery $\textbf{T}$ickets ($\textbf{AdaGLT}$). Our proposed method derives its key advantages and addresses the above limitations through the following three aspects: 1) tailoring layer-adaptive sparse structures for various datasets and GNNs, thus endowing it with the capability to facilitate deeper GNNs; 2) integrating the pruning and training processes, thereby achieving a dynamic workflow encompassing both pruning and restoration; 3) automatically capturing graph lottery tickets across diverse sparsity levels, obviating the necessity for extensive pruning parameter tuning. More importantly, we rigorously provide theoretical proofs to guarantee $\textbf{AdaGLT}$ to mitigate over-smoothing issues and obtain improved sparse structures in deep GNN scenarios. Extensive experiments demonstrate that $\textbf{AdaGLT}$ outperforms state-of-the-art competitors across multiple graph datasets of various scales and types, particularly in scenarios involving deep GNNs.
Reinforcement Learning · Inverse
Adversarial imitation learning (AIL) has stood out as a dominant framework across various imitation learning (IL) applications, with Discriminator Actor Critic (DAC) demonstrating the effectiveness of off-policy learning algorithms in improving sample efficiency and scalability to higher-dimensional observations. Despite DAC’s empirical success, the original AIL objective is on-policy and DAC’s ad-hoc application of off-policy training does not guarantee successful imitation. Follow-up work such as ValueDICE tackles this issue by deriving a fully off-policy AIL objective. Instead in this work, we develop a novel and principled AIL algorithm via the framework of boosting. Like boosting, our new algorithm, AILBoost, maintains an ensemble of weighted weak learners (i.e., policies) and trains a discriminator that witnesses the maximum discrepancy between the distributions of the ensemble and the expert policy. We maintain a weighted replay buffer to represent the state-action distribution induced by the ensemble, allowing us to train discriminators using the entire data collected so far. Empirically, we evaluate our algorithm on both controller state-based and pixel-based environments from the DeepMind Control Suite. AILBoost outperforms DAC on both types of environments, demonstrating the benefit of properly weighting replay buffer data for off-policy training. On state-based environments, AILBoost outperforms ValueDICE and IQ-Learn, achieving state-of-the-art performance with as little as one expert trajectory.
Optimization · First-order
Lipschitz constant estimation plays an important role in understanding generalization, robustness, and fairness in deep learning. Unlike naive bounds based on the network weight norm product, semidefinite programs (SDPs) have shown great promise in providing less conservative Lipschitz bounds with polynomial-time complexity guarantees. However, due to the memory consumption and running speed, standard SDP algorithms cannot scale to modern neural network architectures. In this paper, we transform the SDPs for Lipschitz constant estimation into an eigenvalue optimization problem, which aligns with the modern large-scale optimization paradigms based on first-order methods. This is amenable to autodiff frameworks such as PyTorch and TensorFlow, requiring significantly less memory than standard SDP algorithms. The transformation also allows us to leverage various existing numerical techniques for eigenvalue optimization, opening the way for further memory improvement and computational speedup. The essential technique of our eigenvalue-problem transformation is to introduce redundant quadratic constraints and then utilize both Lagrangian and Shor's SDP relaxations under a certain trace constraint. Notably, our numerical study successfully scales the SDP-based Lipschitz constant estimation to address large neural networks on ImageNet. Our numerical examples on CIFAR10 and ImageNet demonstrate that our technique is more scalable than existing approaches. Our code is available at https://github.com/z1w/LipDiff.
Theory · Optimization
Asynchronous federated learning, which enables local clients to send their model update asynchronously to the server without waiting for others, has recently emerged for its improved efficiency and scalability over traditional synchronized federated learning. In this paper, we study how the asynchronous delay affects the convergence of asynchronous federated learning under non-i.i.d. distributed data across clients. Through the theoretical convergence analysis of one representative asynchronous federated learning algorithm under standard nonconvex stochastic settings, we show that the asynchronous delay can largely slow down the convergence, especially with high data heterogeneity. To further improve the convergence of asynchronous federated learning under heterogeneous data distributions, we propose a novel asynchronous federated learning method with a cached update calibration. Specifically, we let the server cache the latest update for each client and reuse these variables for calibrating the global update at each round. We theoretically prove the convergence acceleration for our proposed method under nonconvex stochastic settings. Extensive experiments on several vision and language tasks demonstrate our superior performances compared to other asynchronous federated learning baselines.
Social Aspects · Fairness, Equity, Justice and Safety
Excellent tail performance is crucial for modern machine learning tasks, such as algorithmic fairness, class imbalance, and risk-sensitive decision making, as it ensures the effective handling of challenging samples within a dataset. Tail performance is also a vital determinant of success for personalized recommender systems to reduce the risk of losing users with low satisfaction. This study introduces a "safe" collaborative filtering method that prioritizes recommendation quality for less-satisfied users rather than focusing on the average performance. Our approach minimizes the conditional value at risk (CVaR), which represents the average risk over the tails of users' loss. To overcome computational challenges for web-scale recommender systems, we develop a robust yet practical algorithm that extends the most scalable method, implicit alternating least squares (iALS). Empirical evaluation on real-world datasets demonstrates the excellent tail performance of our approach while maintaining competitive computational efficiency.
Deep Learning · Generative Models and Autoencoders
Modern distribution matching algorithms for training diffusion or flow models directly prescribe the time evolution of the marginal distributions between two boundary distributions. In this work, we consider a generalized distribution matching setup, where these marginals are only implicitly described as a solution to some task-specific objective function. The problem setup, known as the Generalized Schrödinger Bridge (GSB), appears prevalently in many scientific areas both within and without machine learning. We propose Generalized Schödinger Bridge Matching (GSBM), a new matching algorithm inspired by recent advances, generalizing them beyond kinetic energy minimization and to account for nonlinear state costs. We show that such a generalization can be cast as solving conditional stochastic optimal control, for which efficient variational approximations can be used, and further debiased with the aid of path integral theory. Compared to prior methods for solving GSB problems, our GSBM algorithm always preserves a feasible transport map between the boundary distributions throughout training, thereby enabling stable convergence and significantly improved scalability. We empirically validate our claims on an extensive suite of experimental setups, including crowd navigation, opinion depolarization, LiDAR manifolds, and image domain transfer. Our work brings new algorithmic opportunities for training diffusion models enhanced with task-specific optimality structures.
Reinforcement Learning · Multi-agent
The process of revising (or constructing) a policy at execution time---known as decision-time planning---has been key to achieving superhuman performance in perfect-information games like chess and Go. A recent line of work has extended decision-time planning to imperfect-information games, leading to superhuman performance in poker. However, these methods involve solving subgames whose sizes grow quickly in the amount of non-public information, making them unhelpful when the amount of non-public information is large.Motivated by this issue, we introduce an alternative framework for decision-time planning that is not based on solving subgames, but rather on update equivalence. In this update-equivalence framework, decision-time planning algorithms replicate the updates of last-iterate algorithms, which need not rely on public information. This facilitates scalability to games with large amounts of non-public information. Using this framework, we derive a provably sound search algorithm for fully cooperative games based on mirror descent and a search algorithm for adversarial games based on magnetic mirror descent. We validate the performance of these algorithms in cooperative and adversarial domains, notably in Hanabi, the standard benchmark for search in fully cooperative imperfect-information games. Here, our mirror descent approach exceeds or matches the performance of public information-based search while using two orders of magnitude less search time. This is the first instance of a non-public-information-based algorithm outperforming public-information-based approaches in a domain they have historically dominated.
Miscellaneous Aspects of Machine Learning · General Machine Learning Techniques
It is often advantageous to train models on a subset of the available train examples, because the examples are of variable quality or because one would like to train with fewer examples, without sacrificing performance. We present Gradient Information Optimization (GIO), a scalable, task-agnostic approach to this data selection problem that requires only a small set of (unlabeled) examples representing a target distribution. GIO begins from a natural, information-theoretic objective that is intractable in practice. Our contribution is in showing that it can be made highly scalable through a simple relaxation of the objective and a highly efficient implementation. In experiments with machine translation, spelling correction, and image recognition, we show that GIO delivers outstanding results with very small train sets. These findings are robust to different representation models and hyperparameters for GIO itself. GIO is task- and domain-agnostic and can be applied out-of-the-box to new datasets and domains. We open source a pip-installable implementation of the algorithm as "pip install grad-info-opt".
Reinforcement Learning · Deep RL
Discrete-action reinforcement learning algorithms often falter in tasks with high-dimensional discrete action spaces due to the vast number of possible actions. A recent advancement leverages value-decomposition, a concept from multi-agent reinforcement learning, to tackle this challenge. This study delves deep into the effects of this value-decomposition, revealing that whilst it curtails the over-estimation bias inherent to Q-learning algorithms, it amplifies target variance. To counteract this, we present an ensemble of critics to mitigate target variance. Moreover, we introduce a regularisation loss that helps to mitigate the effects that exploratory actions in one dimension can have on the value of optimal actions in other dimensions. Our novel algorithm, REValueD, tested on discretised versions of the DeepMind Control Suite tasks, showcases superior performance, especially in the challenging humanoid and dog tasks. We further dissect the factors influencing REValueD's performance, evaluating the significance of the regularisation loss and the scalability of REValueD with increasing sub-actions per dimension.
Deep Learning · Graph Neural Networks
Graph neural networks (GNNs) have achieved remarkable success across a wide range of applications, such as recommendation, drug discovery, and question answering. Behind the success of GNNs lies the backpropagation (BP) algorithm, which is the de facto standard for training deep neural networks (NNs). However, despite its effectiveness, BP imposes several constraints, which are not only biologically implausible, but also limit the scalability, parallelism, and flexibility in learning NNs. Examples of such constraints include storage of neural activities computed in the forward pass for use in the subsequent backward pass, and the dependence of parameter updates on non-local signals. To address these limitations, the forward-forward algorithm (FF) was recently proposed as an alternative to BP in the image classification domain, which trains NNs by performing two forward passes over positive and negative data. Inspired by this advance, we propose ForwardGNN in this work, a new forward learning procedure for GNNs, which avoids the constraints imposed by BP via an effective layer-wise local forward training. ForwardGNN extends the original FF to deal with graph data and GNNs, and makes it possible to operate without generating negative inputs (hence no longer forward-forward). Further, ForwardGNN enables each layer to learn from both the bottom-up and top-down signals without relying on the backpropagation of errors. Extensive experiments on real-world datasets show the effectiveness and generality of the proposed forward graph learning framework. We release our code at https://github.com/facebookresearch/forwardgnn.
Deep Learning · Large Language Models
Language models are currently trained to predict tokens given document prefixes, enabling them to zero shot long form generation and prompting-style tasks which can be reduced to document completion. We instead present IN-CONTEXT PRETRAINING, a new approach where language models are trained on a sequence of related documents, thereby explicitly encouraging them to read and reason across document boundaries. Our approach builds on the fact that current pipelines train by concatenating random sets of shorter documents to create longer context windows; this improves efficiency even though the prior documents provide no signal for predicting the next document. Given this fact, we can do IN-CONTEXT PRETRAINING by simply changing the document ordering so that each context contains related documents, and directly applying existing pretraining pipelines. However, this document sorting problem is challenging. There are billions of documents and we would like the sort to maximize contextual similarity for every document without repeating any data. To do this, we introduce approximate algorithms for finding related documents with efficient nearest neighbor search and constructing coherent batches with a graph cover algorithm. Our experiments show IN-CONTEXT PRETRAINING offers a scalable and simple approach to significantly enhance LM performance: we see notable improvements in tasks that require more complex contextual reasoning, including in-context learning (+8%), reading comprehension (+15%), faithfulness to previous contexts (+16%), long-context reasoning (+5%), and retrieval augmentation (+9%).
Miscellaneous Aspects of Machine Learning · Scalable Algorithms
This paper investigates efficient deep neural networks (DNNs) to replace dense unstructured weight matrices with structured ones that possess desired properties. The challenge arises because the optimal weight matrix structure in popular neural network models is obscure in most cases and may vary from layer to layer even in the same network. Prior structured matrices proposed for efficient DNNs were mostly hand-crafted without a generalized framework to systematically learn them. To address this issue, we propose a generalized and differentiable framework to learn efficient structures of weight matrices by gradient descent. We first define a new class of structured matrices that covers a wide range of structured matrices in the literature by adjusting the structural parameters. Then, the frequency-domain differentiable parameterization scheme based on the Gaussian-Dirichlet kernel is adopted to learn the structural parameters by proximal gradient descent. On the image and language tasks, our method learns efficient DNNs with structured matrices, achieving lower complexity and/or higher performance than prior approaches that employ low-rank, block-sparse, or block-low-rank matrices.
Reinforcement Learning · Inverse
Inverse reinforcement learning (IRL) offers a powerful and general framework for learning humans' latent preferences in route recommendation, yet no approach has successfully addressed planetary-scale problems with hundreds of millions of states and demonstration trajectories. In this paper, we introduce scaling techniques based on graph compression, spatial parallelization, and improved initialization conditions inspired by a connection to eigenvector algorithms. We revisit classic IRL methods in the routing context, and make the key observation that there exists a trade-off between the use of cheap, deterministic planners and expensive yet robust stochastic policies. This insight is leveraged in Receding Horizon Inverse Planning (RHIP), a new generalization of classic IRL algorithms that provides fine-grained control over performance trade-offs via its planning horizon. Our contributions culminate in a policy that achieves a 16-24% improvement in route quality at a global scale, and to the best of our knowledge, represents the largest published study of IRL algorithms in a real-world setting to date. We conclude by conducting an ablation study of key components, presenting negative results from alternative eigenvalue solvers, and identifying opportunities to further improve scalability via IRL-specific batching strategies.
Miscellaneous Aspects of Machine Learning · Scalable Algorithms
Recent advances in large language model (LLM) pretraining have led to high-quality LLMs with impressive abilities. By compressing such LLMs via quantization to 3-4 bits per parameter, they can fit into memory-limited devices such as laptops and mobile phones, enabling personalized use. Quantizing models to 3-4 bits per parameter can lead to moderate to high accuracy losses, especially for smaller models (1-10B parameters), which are suitable for edge deployment. To address this accuracy issue, we introduce the Sparse-Quantized Representation (SpQR), a new compressed format and quantization technique that enables for the first time \emph{near-lossless} compression of LLMs across model scales while reaching similar compression levels to previous methods. SpQR works by identifying and isolating \emph{outlier weights}, which cause particularly large quantization errors, and storing them in higher precision while compressing all other weights to 3-4 bits, and achieves relative accuracy losses of less than $1\%$ in perplexity for highly-accurate LLaMA and Falcon LLMs. This makes it possible to run a 33B parameter LLM on a single 24 GB consumer GPU without performance degradation at 15\% speedup, thus making powerful LLMs available to consumers without any downsides. SpQR comes with efficient algorithms for both encoding weights into its format, as well as decoding them efficiently at runtime. Specifically, we provide an efficient GPU inference algorithm for SpQR, which yields faster inference than 16-bit baselines at similar accuracy while enabling memory compression gains of more than 4x.
Theory · Reinforcement Learning and Planning
In reinforcement learning (RL), rewards of states are typically considered additive, and following the Markov assumption, they are independent of states visited previously. In many important applications, such as coverage control, experiment design and informative path planning, rewards naturally have diminishing returns, i.e., their value decreases in light of similar states visited previously. To tackle this, we propose Submodular RL (subRL), a paradigm which seeks to optimize more general, non-additive (and history-dependent) rewards modelled via submodular set functions, which capture diminishing returns. Unfortunately, in general, even in tabular settings, we show that the resulting optimization problem is hard to approximate. On the other hand, motivated by the success of greedy algorithms in classical submodular optimization, we propose subPO, a simple policy gradient-based algorithm for subRL that handles non-additive rewards by greedily maximizing marginal gains. Indeed, under some assumptions on the underlying Markov Decision Process (MDP), subPO recovers optimal constant factor approximations of submodular bandits. Moreover, we derive a natural policy gradient approach for locally optimizing subRL instances even in large state- and action- spaces. We showcase the versatility of our approach by applying subPO to several applications, such as biodiversity monitoring, Bayesian experiment design, informative path planning, and coverage maximization. Our results demonstrate sample efficiency, as well as scalability to high-dimensional state-action spaces.
Social Aspects · Trustworthy Machine Learning
The aligned Large Language Models (LLMs) are powerful language understanding and decision-making tools that are created through extensive alignment with human feedback. However, these large models remain susceptible to jailbreak attacks, where adversaries manipulate prompts to elicit malicious outputs that should not be given by aligned LLMs. Investigating jailbreak prompts can lead us to delve into the limitations of LLMs and further guide us to secure them. Unfortunately, existing jailbreak techniques suffer from either (1) scalability issues, where attacks heavily rely on manual crafting of prompts, or (2) stealthiness problems, as attacks depend on token-based algorithms to generate prompts that are often semantically meaningless, making them susceptible to detection through basic perplexity testing. In light of these challenges, we intend to answer this question: Can we develop an approach that can automatically generate stealthy jailbreak prompts? In this paper, we introduce AutoDAN, a novel jailbreak attack against aligned LLMs. AutoDAN can automatically generate stealthy jailbreak prompts by the carefully designed hierarchical genetic algorithm. Extensive evaluations demonstrate that AutoDAN not only automates the process while preserving semantic meaningfulness, but also demonstrates superior attack strength in cross-model transferability, and cross-sample universality compared with the baseline. Moreover, we also compare AutoDAN with perplexity-based defense methods and show that AutoDAN can bypass them effectively. Code is available at https://github.com/SheltonLiu-N/AutoDAN.
Miscellaneous Aspects of Machine Learning · Scalable Algorithms
We employ random matrix theory to establish consistency of generalized cross validation (GCV) for estimating prediction risks of sketched ridge regression ensembles, enabling efficient and consistent tuning of regularization and sketching parameters. Our results hold for a broad class of asymptotically free sketches under very mild data assumptions. For squared prediction risk, we provide a decomposition into an unsketched equivalent implicit ridge bias and a sketching-based variance, and prove that the risk can be globally optimized by only tuning sketch size in infinite ensembles. For general subquadratic prediction risk functionals, we extend GCV to construct consistent risk estimators, and thereby obtain distributional convergence of the GCV-corrected predictions in Wasserstein-2 metric. This in particular allows construction of prediction intervals with asymptotically correct coverage conditional on the training data. We also propose an "ensemble trick" whereby the risk for unsketched ridge regression can be efficiently estimated via GCV using small sketched ridge ensembles. We empirically validate our theoretical results using both synthetic and real large-scale datasets with practical sketches including CountSketch and subsampled randomized discrete cosine transforms.
Deep Learning · Algorithms
We introduce the concept of scalable neural network kernels (SNNKs), the replacements of regular feedforward layers (FFLs), capable of approximating the latter, but with favorable computational properties. SNNKs effectively disentangle the inputs from the parameters of the neural network in the FFL, only to connect them in the final computation via the dot-product kernel. They are also strictly more expressive, as allowing to model complicated relationships beyond the functions of the dot-products of parameter-input vectors. We also introduce the neural network bundling process that applies SNNKs to compactify deep neural network architectures, resulting in additional compression gains. In its extreme version, it leads to the fully bundled network whose optimal parameters can be expressed via explicit formulae for several loss functions (e.g. mean squared error), opening a possibility to bypass backpropagation. As a by-product of our analysis, we introduce the mechanism of the universal random features (or URFs), applied to instantiate several SNNK variants, and interesting on its own in the context of scalable kernel methods. We provide rigorous theoretical analysis of all these concepts as well as an extensive empirical evaluation, ranging from point-wise kernel estimation to Transformers' fine-tuning with novel adapter layers inspired by SNNKs. Our mechanism provides up to 5x reduction in the number of trainable parameters, while maintaining competitive accuracy.
Reinforcement Learning · Deep RL
TD-MPC is a model-based reinforcement learning (RL) algorithm that performs local trajectory optimization in the latent space of a learned implicit (decoder-free) world model. In this work, we present TD-MPC2: a series of improvements upon the TD-MPC algorithm. We demonstrate that TD-MPC2 improves significantly over baselines across 104 online RL tasks spanning 4 diverse task domains, achieving consistently strong results with a single set of hyperparameters. We further show that agent capabilities increase with model and data size, and successfully train a single 317M parameter agent to perform 80 tasks across multiple task domains, embodiments, and action spaces. We conclude with an account of lessons, opportunities, and risks associated with large TD-MPC2 agents.Explore videos, models, data, code, and more at https://tdmpc2.com